Question:
The lateral surface area of a cube is 900 cm2. Find its volume.
Solution:
Suppose that the side of cube is x cm.
Lateral surface area of the cube = 900 cm2.
Then $900=4 x^{2}$
$\Rightarrow x^{2}=\frac{900}{4}=225$
$\Rightarrow x=\sqrt{225}=15$
i.e., the side of the cube is 15 cm.
$\therefore$ Volume of the given cube $=x^{3} \mathrm{~cm}^{3}=15^{3} \mathrm{~cm}^{3}=3375 \mathrm{~cm}^{3}$